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Electronically steerable parasitic array radiator (ESPAR) technology enables the implementation of antenna arrays of a number of elements with a single radio frequency (RF) source. Two approaches to achieve stable transmission using an ESPAR antenna (EA) are to increase the self-resistance of an EA or to transmit signals closely approximating the actual signals that keep the EA stable. Both approaches did not take into account the impact of limited power on an EA transmission, which is a practical constraint on power amplifier design. We propose a new transmission scheme to enable an EA to provide stable multiple antenna functionality taking into account the instantaneous total power requirement. This problem is formulated as a non-convex optimization problem and it is solved analytically by coordinate transformation and geometric analysis. The optimal approximate signals are obtained using root finding and interior-point algorithms. Moreover, it is shown through simulations that our proposed scheme achieves similar symbol error rate performance to that of the standard multiple antenna transmitter with multiple RF chains under power limited single-user and multi-user transmission scenarios. Furthermore, it is shown that increasing the self-resistance of an EA to achieve stability is highly power inefficient.
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